This invention relates to an apparatus for machining a non-circular workpiece wherein a workpiece is rotated at a constant angular velocity .omega. and a cutting tool is moved in a direction perpendicular to the rotational axis of the workpiece and a direction parallel to the rotational axis in a synchronized relationship with rotation of the workpiece so that the workpiece may be machined into a non-circular shape whose sectional shape changes along the rotational axis.
In case that a difference between major and minor diameters of a workpiece is constant at all positions along the rotational axis of the workpiece, only one set of non-circular profile data (hereinafter referred to as profile data), which defines a sectional shape perpendicular to the rotational axis of the workpiece, is required to be prepared. In this case, profile data of other sections can be calculated based on the prepared profile data with taking the major and minor diameters of each section into consideration.
However, prior apparatus for machining the non-circular workpiece wherein profile data of a predetermined section of the workpiece is stored and the profile data of the other sections are created based upon the periodicity of the sectional shape has a problem in that the apparatus cannot machine the workpiece whose difference between the major and the minor diameter doesn't vary constantly with respect to the axial position along the rotational axis of the workpiece and the workpiece which twists with respect to the axis of the workpiece, because the profile data of the other sections cannot be created by the calculation based on the stored profile data for the predetermined section of the workpiece.